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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 259920.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259920.u1 | 259920u1 | \([0, 0, 0, 1805858097, 18438523765598]\) | \(569208099614384/457763671875\) | \(-523775074445733867187500000000\) | \([]\) | \(294174720\) | \(4.3904\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 259920.u1 has rank \(1\).
Complex multiplication
The elliptic curves in class 259920.u do not have complex multiplication.Modular form 259920.2.a.u
sage: E.q_eigenform(10)